Nature's morphology and optimal energetic solutions remain the key motivation for designing cellular-based lattice structures. Understanding the nonlinear dynamical behaviors that arise from different lattice topologies of such structures in the metastructure framework is crucial for their successful implementation in various novel designs and technologies related to vibration and shape control. This paper presents a study of the static and dynamic response of auxetic and honeycomb lattices with hourglass or dome-shaped metastructures. The potential tailoring of nonlinearity of such responses through various design parameters that play a vital role in shaping the dynamic properties of such structures is discussed here. The impact of cell design parameters on the resulting macroscopic behavior is assessed using both numerical simulations and experimental studies. The transition from softening to hardening nonlinear dynamic responses is reported with cell topologies ranging from the regular honeycomb to auxetic topologies that are widely used as fundamental cells of cellular materials design. The experimental study is based on the time responses measured to verify the numerical predictions. The experimental system consists of different 3D printed hourglass samples based on the auxetic and honeycomb lattices on which dynamic testing using a laser Doppler vibrometer is performed. The design strategies proposed in this paper can be integrated into a wide range of lattice-based materials for noise and vibration control applications and biomedical devices.

The shape memory effect (SME) is a source of internal compressive stresses that modify the vibration behavior of shape memory alloy (SMA) embedded composite structures. Generally, long fibers are used due to their suitability for activating SMA using resistive heating. Longer SMA fibers embedded in composite structures have their limitations in design and manufacturing. Minimal research work has been done on tuning the vibration behavior of composite structures embedded with short SMA fibers. In this research paper, an analytical model for evaluating the natural frequencies of an SMA embedded composite beam has been proposed. Effects of various design parameters for long (continuous) and short (discontinuous) SMA fibers embedded in composites have been investigated. It was observed that short SMA fibers with a higher aspect ratio can tune their frequencies similarly to long SMA fiber composites and are more effective in thicker beams. Matrix material with negative coefficient thermal expansion is more suitable for embedding SMA for modifying natural frequency in active mode.

The auxetic meta-material is a special class of macro-structure designed for exhibiting negative Poisson's ratio. The spatial repetition of the lattice affects the wave propagation and dynamic responses. In this study, a mathematical basis of Bloch analysis for auxetic media have been presented and shaded some important light on the application of the technique. For this design an analysis has been carried out to show how the periodic boundary condition changes with the connectivity, orientation and geometry of unit lattice. The corresponding eigen value problem is developed to obtain the propagation frequency which is the function of mass, stiffness matrix and the wave vector. Mapping of different forms which are associated with the nodal displacements of a unit cell to adjacent cell have been demonstrated and formulated mathematically and observed its effect on the reduced stiffness and mass matrices is studied. Modal analysis has been carried out using Abaqus 6.14 and the transverse nodal displacements obtained from the F.E analysis. The Bloch formulation for revolving-square type auxetic structure has been formulated and validated. Further, we have obtained the changes in auxetic behavior of the structure under different boundary conditions. The periodicity of a given lattice assists in determining the frequency bands within which the propagation of elastic waves is permitted. Further study is proposed for attenuation and transmission band analysis to steer the waves which roots the idea of vibration sink, in which we can damp the mechanical waves effectively at a specific location. The Auxetic meta-materials is envisaged to have a significant role in wave attenuation and wave steering, and can be used effectively for vibration control.